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94 the abstraction of

94 the abstraction of the accepted gaps only. If the two models give equally satisfactory predictions, the simple linear model would be easier to apply since it involves less labour in abstracting the data. The 'models tested with the Armitage and McDonald method are the following: (1) A weighted linear model assuming the gap size, T, as the dependent variable, and the number of entries, N, as the independent variable. (2) An unweighted linear model, SRTN assuming the same dependent and independent variables as in (1). (3) An unweighted linear model, SRNT, with the dependency inverted. The reason that another weighted model was not used was that, as section 4.5.5 demonstrated, the performance of the two weighted models was similar. The test was carried out on computer simulation data generated using 5 sets of initial values. Tables 4.18, 4.19, 4.20, 4.21, 4.22 include the detailed results of the analysis of each group of the simulated data using tie Arinitage and McDonald method. The comparison is summarised in Tables 4.23 and 4.24. Table 4.23 includes the mean values and standard deviations of the predicons over all the simulated data groups of each input values set, for all 4 methods of analysis. Comparison of the mean value of the predictions demonstrates that the method provided by far the best results is the weighted linear model. This can be seen in Fig. 4.7 for the predictions of the critical gap and in Fig. 4.9 for the move-up time. For the critical gap, the weighted linear model gives the best prediction in all five cases; while for the move-up time, it gives the best prediction in two cases. The main problem of this method is the very high standard deviations associated with the predictions. This is

95 demonstrated on Fig. 4.8 and Fig. 4.10. Therefore, the predictions derived from any one group of data is very likely to vary from the true value. This becomes very important when the method is applied on observed data; in such cases the number of data points available is restricted compared with simulated data. The other three methods had much lower standard deviations, of a similar order. These three methods are compared in Table 4.24. Since the standard deviations were of a similar order only the means are compared. The Armitage and McDonald method consistently overestimates a, the range of percentage over- estimations is 3.3% - 6%. The linear models consistently underestimate a, SRTN by -4.0% to -7% and SRNT by -8.7% to -15.7%. The predictions of are much better, the Armitage and McDonald method underestimates by -1.6% to -5.0%, SRTN has a range of -1.0% to +1.1%, while SRNT overestimates by 3.2% to 10.4%, SRNT provides the worst predictions in both cases. The other two methods predict values much closer to the input values. According to the criteria set out in the beginning of the section the linear model SRTN was adopted for the analysis of the data collected for this study. 4.7 Application of the Simple Linear Model on Observed Data The simple linear model described in the previous sections was applied to the data collected from the three roundabouts in Sheffield as described in Chapter 3. As the data abstracted were separated into gap acceptanc for each lane, the model was applied separately on each lane providing parameters in each case. The values arrived at are included in Table 4.25. As can be seen, the results show some difference